%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : KLE150+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:43:41 AM UTC 2026
% Result : Theorem 51.43s 7.18s
% Output : CNFRefutation 51.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 20 unt; 0 def)
% Number of atoms : 40 ( 21 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 13 ~; 7 |; 2 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 1 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [X0,X1] : addition(X0,X1) = addition(X1,X0) ).
fof(idempotence,axiom,
! [X0] : addition(X0,X0) = X0 ).
fof(multiplicative_associativity,axiom,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2) ).
fof(left_annihilation,axiom,
! [X0] : multiplication(zero,X0) = zero ).
fof(star_unfold1,axiom,
! [X0] : addition(one,multiplication(X0,star(X0))) = star(X0) ).
fof(infty_unfold1,axiom,
! [X0] : 'strong$uiteration'(X0) = addition(multiplication(X0,'strong$uiteration'(X0)),one) ).
fof(order,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> addition(X0,X1) = X1 ) ).
fof(goals,conjecture,
! [X0] :
( leq(addition(one,multiplication(X0,zero)),'strong$uiteration'(multiplication(X0,zero)))
& leq('strong$uiteration'(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) ) ).
fof(negated_conjecture,negated_conjecture,
~ ! [X0] :
( leq(addition(one,multiplication(X0,zero)),'strong$uiteration'(multiplication(X0,zero)))
& leq('strong$uiteration'(multiplication(X0,zero)),addition(one,multiplication(X0,zero))) ),
inference(negate_conjecture,[status(cth)],[goals]) ).
cnf(c0,plain,
addition(X0,X1) = addition(X1,X0),
inference(clausification,[status(esa)],[additive_commutativity]) ).
cnf(c3,plain,
addition(X0,X0) = X0,
inference(clausification,[status(esa)],[idempotence]) ).
cnf(c4,plain,
multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(clausification,[status(esa)],[multiplicative_associativity]) ).
cnf(c9,plain,
multiplication(zero,X0) = zero,
inference(clausification,[status(esa)],[left_annihilation]) ).
cnf(c10,plain,
addition(one,multiplication(X0,star(X0))) = star(X0),
inference(clausification,[status(esa)],[star_unfold1]) ).
cnf(c14,plain,
'strong$uiteration'(X0) = addition(multiplication(X0,'strong$uiteration'(X0)),one),
inference(clausification,[status(esa)],[infty_unfold1]) ).
cnf(c18,plain,
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(clausification,[status(esa)],[order]) ).
cnf(c19,plain,
( ~ leq(addition(one,multiplication(sK34,zero)),'strong$uiteration'(multiplication(sK34,zero)))
| ~ leq('strong$uiteration'(multiplication(sK34,zero)),addition(one,multiplication(sK34,zero))) ),
inference(clausification,[status(esa)],[negated_conjecture]) ).
cnf(d0,plain,
addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))) = star(multiplication(X0,X1)),
inference(superposition,[status(thm)],[c4,c10]) ).
cnf(d1,plain,
addition(one,multiplication(X0,zero)) = star(multiplication(X0,zero)),
inference(superposition,[status(thm)],[c9,d0]) ).
cnf(d2,plain,
'strong$uiteration'(X0) = addition(one,multiplication(X0,'strong$uiteration'(X0))),
inference(demodulation,[status(thm)],[c14,c0]) ).
cnf(d3,plain,
'strong$uiteration'(multiplication(X0,X1)) = addition(one,multiplication(X0,multiplication(X1,'strong$uiteration'(multiplication(X0,X1))))),
inference(superposition,[status(thm)],[c4,d2]) ).
cnf(d4,plain,
'strong$uiteration'(multiplication(X0,zero)) = addition(one,multiplication(X0,zero)),
inference(superposition,[status(thm)],[c9,d3]) ).
cnf(d5,plain,
'strong$uiteration'(multiplication(X0,zero)) = star(multiplication(X0,zero)),
inference(demodulation,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( ~ leq('strong$uiteration'(multiplication(sK34,zero)),addition(one,multiplication(sK34,zero)))
| ~ leq(star(multiplication(sK34,zero)),'strong$uiteration'(multiplication(sK34,zero))) ),
inference(demodulation,[status(thm)],[c19,d1]) ).
cnf(d7,plain,
( ~ leq('strong$uiteration'(multiplication(sK34,zero)),star(multiplication(sK34,zero)))
| ~ leq(star(multiplication(sK34,zero)),'strong$uiteration'(multiplication(sK34,zero))) ),
inference(demodulation,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
( ~ leq('strong$uiteration'(multiplication(sK34,zero)),star(multiplication(sK34,zero)))
| ~ leq(star(multiplication(sK34,zero)),star(multiplication(sK34,zero))) ),
inference(demodulation,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ leq(star(multiplication(sK34,zero)),star(multiplication(sK34,zero)))
| ~ leq(star(multiplication(sK34,zero)),star(multiplication(sK34,zero))) ),
inference(demodulation,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
( leq(X0,X0)
| X0 != X0 ),
inference(superposition,[status(thm)],[c3,c18]) ).
cnf(d11,plain,
leq(X0,X0),
inference(equality_resolution,[status(thm)],[d10]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE150+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n003.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Fri Sep 25 19:29:22 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 51.43/7.18 % SZS status Theorem for theBenchmark.p
% 51.43/7.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------